YouTube is now what TV used to be. So yes, you should be able to show this content. However, the platform needs to provide betyer tools to users and producers to aide in categorizing content.
I saw plenty of different views of folks being injured or killed in recent protests on the television, I saw folks losing their lives in Nice recently on television, I saw a reporter shot point blank in 2015 on television, I saw an old man shot to death from the point of view of the killer earlier this year on television.
And that's not even counting war footage.
I'm not hunting this stuff down, the only protection against watching this crap is a half second pause after the reporter says "Warning, the following may be considered graphic."
The funny thing is : I don't own a television; I just go to a diner with whatever garbage news channel everyone in the place likes at any given time for breakfast occasionally. Even brief casual glimpses at any given news channel are bound to get you an eye-full of gore or violence of some sort.
I dont think its about morals, but more about userbase expectations. YouTube as a product is generally seen as a video archive. They do have the choice to not host it, but they risk an user exodus. Given the competition from Facebook, Snapchat, and the like, that's a risk they cant take. More so when it's Alphabet's only successful social network acquisition.